@article {12612,
	title = {Principal components null space analysis for image and video classification},
	journal = {Image Processing, IEEE Transactions on},
	volume = {15},
	year = {2006},
	month = {2006/07//},
	pages = {1816 - 1830},
	abstract = {We present a new classification algorithm, principal component space analysis (PCNSA), which is designed for classification problems like object recognition where different classes have unequal and nonwhite noise covariance matrices. PCNSA first obtains a principal components subspace (PCA space) for the entire data. In this PCA space, it finds for each class "i", an M<sub>i</sub>-dimensional subspace along which the class{\textquoteright} intraclass variance is the smallest. We call this subspace an approximate space (ANS) since the lowest variance is usually "much smaller" than the highest. A query is classified into class "i" if its distance from the class{\textquoteright} mean in the class{\textquoteright} ANS is a minimum. We derive upper bounds on classification error probability of PCNSA and use these expressions to compare classification performance of PCNSA with that of subspace linear discriminant analysis (SLDA). We propose a practical modification of PCNSA called progressive-PCNSA that also detects "new" (untrained classes). Finally, we provide an experimental comparison of PCNSA and progressive PCNSA with SLDA and PCA and also with other classification algorithms-linear SVMs, kernel PCA, kernel discriminant analysis, and kernel SLDA, for object recognition and face recognition under large pose/expression variation. We also show applications of PCNSA to two classification problems in video-an action retrieval problem and abnormal activity detection.},
	keywords = {approximate null space;classification error probability;face recognition;image classification;object recognition;principal components null space analysis;subspace linear discriminant analysis;video classification;image classification;principal component a, Automated;Principal Component Analysis;Signal Processing, Computer-Assisted;Information Storage and Retrieval;Models, Computer-Assisted;Video Recording;, Statistical;Pattern Recognition},
	isbn = {1057-7149},
	doi = {10.1109/TIP.2006.873449},
	author = {Vaswani, N. and Chellapa, Rama}
}
